SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.
1) Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

The sign test compares the signs (negative or positive) of the differences for data sets, ignoring any ties resulting in a difference of zero. The sign test can be used to test claims involving two dependent samples, claims involving nominal data, and claims about the median of a single population. The underlying concept is that if two sets of data have equal medians, the number of positive signs should be approximately equal to the number of negative signs.

2) Describe the Wilcoxon rank-sum test. What type of hypotheses is it used to test? What assumptions are made for this test? What is the underlying concept?

The Wilcoxon rank-sum test looks at ranks but not signs for the data points. The test is used to test claims about the differences between two independent samples. The assumptions include: two randomly selected independent samples; testing the null hypothesis that the two independent samples come from the same distribution; and more than 10 scores in each of the samples. The underlying principle is that if two samples are drawn from identical populations and the individual scores are all ranked as one combined collection of values, then the high and low ranks should fall evenly between the two samples. For example, if low ranks are found predominantly in one sample with the high ranks in the other, then we suspect that the two samples are not identical.

Use the sign test to test the indicated claim.
3) An instructor gives a test before and after a lesson and results from randomly selected students are given below. At the 0.05 level of significance, test the claim that the lesson has no effect on the grade. Use the sign test.

Before

54

61

56

41

38

57

42

71

88

42

36

23

22

46

51

After

82

87

84

76

79

87

42

97

99

74

85

96

69

84

79

H0: There is no difference between before and after grades.
H1: There is a difference between before and after grades.
Test statistic: x = 0. Critical value: x = 2.
Reject the null hypothesis of no difference. There is sufficient evidence to warrant rejection of the claim that the lesson has no effect on grade.

4) A researcher wishes to study whether music has any effect on the ability to memorize
information. 89 randomly selected adults are given a memory test in a quiet room. They are then given a second memory test while listening to classical music. 66 people received a higher score on the second test, 22 a lower score, and 1 received the same score. At the 0.05 significance level, test the claim that the music has no effect on memorization skills.

H0: the music has no effect on memorization skills.
H1: the music has an effect on memorization skills.
Convert x = 22 to the test statistic z = -4.58. Critical values: z = ±1.96.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that music has no effect on memorization skills

Use the Wilcoxon signed-ranks test to test the claim that both samples come from populations having the same distribution.
5) Use the Wilcoxon signed-ranks test and the sample data below. At the 0.05 significance level, test the claim that math and verbal scores are the same.

Mathematics

347

440

327

456

427

349

377

398

425

Verbal

285

378

243

371

340

271

294

322

385

Test statistic T = 0. Critical value: T = 6.
Reject the null hypothesis that both samples come from the same population distribution

Use the Wilcoxon rank-sum test to test the claim that the two independent samples come from the same distribution.
6) Use the Wilcoxon rank-sum approach to test the claim that students at two colleges achieve the same distribution of grade averages. The sample data is listed below. Use a 0.05 level of significance.